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-(x+6)(x+4)=x(x+11+6)-
We move all terms to the left:
-(x+6)(x+4)-(x(x+11+6)-)=0
We add all the numbers together, and all the variables
-(x+6)(x+4)-(x(x+17)-)=0
We multiply parentheses ..
-(+x^2+4x+6x+24)-(x(x+17)-)=0
We calculate terms in parentheses: -(x(x+17)-), so:We get rid of parentheses
x(x+17)-
We add all the numbers together, and all the variables
x(x+17)
We multiply parentheses
x^2+17x
Back to the equation:
-(x^2+17x)
-x^2-x^2-4x-6x-17x-24=0
We add all the numbers together, and all the variables
-2x^2-27x-24=0
a = -2; b = -27; c = -24;
Δ = b2-4ac
Δ = -272-4·(-2)·(-24)
Δ = 537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{537}}{2*-2}=\frac{27-\sqrt{537}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{537}}{2*-2}=\frac{27+\sqrt{537}}{-4} $
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